Revisiting the Immirzi parameter: Landauer's principle and alternative entropy frameworks in Loop Quantum Gravity

This paper investigates the implications from area quantization in Loop Quantum Gravity, particularly focusing on the application of the Landauer principle -- a fundamental thermodynamic concept establishing a connection between information theory and thermodynamics. By leveraging the Landauer principle in conjunction with the Bekenstein-Hawking entropy law, we derive the usual value for the Immirzi parameter precisely, $\gamma = \ln2/(\pi \sqrt{3})$, without using the typical procedure that involves the Boltzmann-Gibbs entropy. Furthermore, following an analogous procedure, we derive a modified expression for the Immirzi parameter aligned with Barrow's entropy formulation. Our analysis also yields a new expression for the Immirzi parameter consistent with a corresponding modified Kaniadakis entropy for black hole entropy further illustrating, along with Barrow's entropy, the applicability of Landauer's principle in alternative statistical contexts within black hole physics.